number lineIt is a fundamental concept in mathematics that specifies the origin, the positive direction, and the unit length of a straight line.
Manimhit the nail on the headNumberLineIt is an object dedicated to representing the numerical axis, which allows the user to set parameters such as the range, interval and display length of the numerical axis, so as to flexibly display one-dimensional numerical changes in mathematics in the animation.
As described belowManimhit the nail on the headNumberLineobjects from basic functions to usage examples.
1. Main parameters
NumberLineA wide range of parameters and customizability are available to meet a wide variety of needs for axis displays.
| Parameter name | typology | clarification |
|---|---|---|
| x_range | Sequence[float] | Range of numerical axis scales |
| length | float | Length of the axes |
| unit_size | float | Distance between scales |
| include_ticks | bool | Scale included or not |
| tick_size | float | Length of the scale mark |
| numbers_with_elongated_ticks | Iterable[float] | List of special scales for stretching |
| longer_tick_multiple | int | Stretch ratio of the stretched scale |
| rotation | float | Angle of rotation of the numerical axis |
| stroke_width | float | Thickness of the numbered axis lines |
| include_tip | bool | Whether the axis contains arrows |
| tip_width | float | Width of arrows |
| tip_height | float | Height of arrows |
| tip_shape | ArrowTip | Types of arrows for numeric axes |
| include_numbers | bool | Whether the scale contains a numerical value |
| scaling | _ScaleBase | Scaling of axes |
| font_size | float | Size of the text on the scale |
| label_direction | Sequence[float] | Orientation of the text on the scale |
| label_constructor | VMobject | Objects that build text on a scale |
| line_to_number_buff | float | Distance between the line of the numerical axis and the text |
| decimal_number_config | dict | Stylized configuration of text on the scale |
| numbers_to_exclude | Iterable[float] | Scale lists that do not require text to be displayed |
| numbers_to_include | Iterable[float] | List of scales for which text needs to be displayed |
There are many parameters, but they are divided into 3 main parts (the axis of thethreads，graduated scalecap (a poem)numerical value) settings.
For example, a parameter name containingticks, which are generally set to the blue part (scale) in the picture above;
The parameter name contains thetipmaybelines, generally set the red line in the picture above as well as the arrowed portion (the numbered axis line);
The parameter name contains thelabelmaybenumbers, which generally set the yellow numbered portion (numerical value) in the above figure.
Other parameters are also relevant to the 3 sections above, and later examples will demonstrate the use of the various parameters.
2. Main approaches
The main methods provided by the numbered axes are:
| name (of a thing) | clarification |
|---|---|
| add_labels | Adding Label Text to Certain Positions on the Axis |
| add_numbers | Adding Values to the Axis |
| add_ticks | Adding a Scale to the Numeric Axis |
| get_labels | Get the label text on the axis |
| get_number_mobject | Getting numeric objects on an axis |
| get_tick | Getting the scale on an axis |
| get_tick_range | Get the scale range on the numeric axis |
| n2p（number_to_point） | Get the position of this value on the numerical axis based on the value |
| p2n（point_to_number） | Get the corresponding value based on the position on the number axis |
These methods are useful when dynamically adding, modifying, and deleting content on an axis.
3. Examples of use
NumberLine (NumberLine) parameters and methods are quite a lot, can not be demonstrated one by one, the following example from the style of the number axis, the
Scale and value settings, and dynamic movement of data points on the axes are demonstrated in several ways.
3.1 Axis size and color
number line（NumberLine(used for emphasis)adults and childrencap (a poem)coloris the most commonly set, the relevant parameters are mainlylength，stroke_widthcap (a poem)color。
# Number lines with different lengths
l1 = NumberLine(
x_range=[-5, 5], length=2, l1 = NumberLine(
length=2, )
)
l2 = NumberLine(
x_range=[-5, 5], length=4, )
length=4, )
)
l3 = NumberLine(
x_range=[-5, 5], length=6, )
length=6, )
)
# Thick, thick, and colorful number line
l4 = NumberLine(
x_range=[-5, 5], stroke_width=1, x_range=[-5, 5], l4 = NumberLine(
stroke_width=1, color=BLUE,
color=BLUE, )
)
l5 = NumberLine(
x_range=[-5, 5], stroke_width=3, color=BLUE, )
stroke_width=3, color=RED, )
color=RED, )
)
l6 = NumberLine(
x_range=[-5, 5], stroke_width=6, color=RED, )
stroke_width=6, color=GREEN, )
color=GREEN, )
)
3.2 Arrowheads for numbered axes
The numeric axes do not have arrows by default, and they can be changed with thetipA related parameter that adds different styles of arrows in the positive direction of the axis.
l1 = NumberLine(
x_range=[-5, 6],
include_tip=True,
tip_width=0.15,
tip_height=0.15,
)
l2 = NumberLine(
x_range=[-5, 6],
include_tip=True,
tip_shape=ArrowCircleTip,
tip_width=0.15,
tip_height=0.15,
)
l3 = NumberLine(
x_range=[-5, 6],
include_tip=True,
tip_shape=ArrowCircleFilledTip,
tip_width=0.15,
tip_height=0.15,
)
l4 = NumberLine(
x_range=[-5, 6],
include_tip=True,
tip_shape=ArrowSquareTip,
tip_width=0.15,
tip_height=0.15,
)
l5 = NumberLine(
x_range=[-5, 6],
include_tip=True,
tip_shape=StealthTip,
tip_width=0.15,
tip_height=0.15,
)
3.3 Scale and value
By default, the number axis on thegraduated scalecap (a poem)numerical valueis displayed sequentially, while the display via thex_rangeparameter, you can set the value interval display;
pass (a bill or inspection etc)scalingparameter, it is possible to display uneven values on equally spaced scales; it is also possible to highlight certain scales.
# Default number line
l1 = NumberLine(
x_range=[-6, 6, 1], )
)
# Number line for numeric intervals
l2 = NumberLine(
x_range=[-6, 6, 2], )
)
# Number is an exponent with a base of 10
l3 = NumberLine(
x_range=[0, 5, 1],
scaling=LogBase(base=10), )
)
# Highlight certain scales
l4 = NumberLine(
x_range=[-6, 6, 1], )
)
[7].set_color(RED).scale(2)
[3].set_color(GREEN).scale(2)
3.4 Data points on the axes
The points on the axes are not the same as the positions displayed on the screen, through the functions provided by the axesn2pcap (a poem)p2n，
It is easy to map points on the screen to the axes and also to calculate their position on the screen based on the points on the axes.
The following animation example first gets its position on the screen based on the value on the axis and then draws the point.
Next, move this point, displaying the value of this point on the numeric axis as you move.
l = NumberLine(
x_range = [-6, 6, 1], )
)
# n2p Get the position of -4 on the screen
p = l.n2p(-4)
d = Dot(p, color=BLUE)
# initial value
txt = MathTex("-4.00")
# p2n Get the value on the numeric axis
txt.add_updater(
lambda x: (
MathTex(
round(l.p2n(d.get_center()), 2),
color=RED,
color=RED, font_size=30,
).next_to(d, UP, buff=0.2)
)
)
# Move this point to see the value change
(.move_to(RIGHT))
4. Neighborhood
The complete code for the article is on a web disk (number_line.py），
Download at.Full Code (Access code: 6872)